A generalization of a theorem of Jacobson

Author:
Susan Montgomery

Journal:
Proc. Amer. Math. Soc. **28** (1971), 366-370

MSC:
Primary 16.58

DOI:
https://doi.org/10.1090/S0002-9939-1971-0276272-5

MathSciNet review:
0276272

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Abstract: A well-known theorem of Jacobson asserts that a ring in which for each in must be commutative. This paper gives a description of a ring with involution in which the above condition is imposed only on the symmetric elements. In particular, if is primitive, is either commutative or the matrices over a field, and, in general, any such is locally finite and satisfies a polynomial identity of degree 8.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0276272-5

Keywords:
Rings with involution,
commutativity,
polynomial identity,
algebraic algebras

Article copyright:
© Copyright 1971
American Mathematical Society